In mathematics, the bisection method is a root-finding method that apply to any continuous functions for which one knows two values with opposite signs. They let extending bisection method into efficient algorithms for finding all real beginnings of a polynomial; see Real-root isolation.
N ← 1 while N ≤ NMAX do // restrict iterations to prevent infinite loop if N ← N + 1 // increment step counter
%The bisection method for finding the root of a function. %f(a) is < 0 and f(b) > 0. By the intermediate value theorem, %there exists a number c in between a and b such that f(c) = 0. %In other words, there is always a root in between f(a) and f(b). %The bisection method takes the midpoint between a and b and evaluates %the value of the function at the midpoint. If it is less than 0, %a is assigned the midpoint. If it is greater than 0, b is assigned the %midpoint. With each iteration, the interval the root lies in is halved, %guaranteeing that the algorithm will converge towards the root. %INPUTS: %Function handle f %endpoint a %endpoint b %maximum tolerated error %OUTPUTS: %An approximated value for the root of f within the defined interval. %Written by MatteoRaso function y = bisection(f, a, b, error) %Making sure that the user didn't input invalid endpoints. if ~(f(a) < 0) disp("f(a) must be less than 0") elseif ~(f(b) > 0) disp("f(b) must be greater than 0") else c = 1e9; %Loops until we reach an acceptable approximation. while abs(f(c)) > error c = (a + b) / 2; if f(c) < 0 a = c; else b = c; endif disp(f(c)) endwhile x = ["The root is approximately located at ", num2str(c)]; disp(x) y = c; endif endfunction